Dao-Qing Dai

Human face recognition using PCA on wavelet subband

Together with the growing interest in the development of human and computer interface and biometric identification, human face recognition has become an active research area since early 1990. Nowadays, principal component analysis (PCA) has been widely adopted as the most promising face recognition algorithm. Yet still, traditional PCA approach has its limitations: poor discrimi- natory power and large computational load. In view of these limita- tions, this article proposed a subband approach in using PCA— apply PCA on wavelet subband. Traditionally, to represent the human face, PCA is performed on the whole facial image. In the proposed method, wavelet transform is used to decompose an im- age into different frequency subbands, and a midrange frequency subband is used for PCA representation. In comparison with the traditional use of PCA, the proposed method gives better recogni- tion accuracy and discriminatory power; further, the proposed method reduces the computational load significantly when the im- age database is large, with more than 256 training images. This article details the design and implementation of the proposed method, and presents the encouraging experimental results.

Regularized discriminant analysis and its application to face recognition

The linear (Fisher) discriminant analysis (LDA) is a well-known and popular statistical method in pattern recognition and classi5cation. The basic idea is to optimize the discriminant criteria, in which the ratio between the interand the intra-class distance is maximized. This approach is theoretically sound and a number of papers have shown its superior performance when applying in pattern-recognition applications [1–5]. However, this approach su;ers from the small-size problem. This problem occurs when the sample size is small compared with the size of feature vector, which always appears in the face-recognition applications. This is because the typical image dimension for face image is greater than 32× 32 and usually, only 2–6 images are used for training. Thus, the within-class covariance estimation Cw will be singular. In this case, the eigenvalue problem is ill-posed. The Fisher index, In(T ), will be reached at the null space of Cw and will always result in in5nity index, In(T ) → ∞. A number of methods have been proposed in the last decade to overcome the limitation of LDA on small sample size. These methods, in applying to face recognition, can be roughly grouped into three categories. The 5rst approach applied a dimension reduction method, such as principal component analysis (PCA), to extract important components for LDA. This approach is straightforward but the dimension reduction method may remove some useful information for recognition. The second approach modi5es the Fisher’s optimization criteria. Theoretically, this approach can solve the problem but the constraints [1–3] will limit the

Kernel machine-based one-parameter regularized Fisher discriminant method for face recognition

This paper addresses two problems in linear discriminant analysis (LDA) of face recognition. The first one is the problem of recognition of human faces under pose and illumination variations. It is well known that the distribution of face images with different pose, illumination, and face expression is complex and nonlinear. The traditional linear methods, such as LDA, will not give a satisfactory performance. The second problem is the small sample size (S3) problem. This problem occurs when the number of training samples is smaller than the dimensionality of feature vector. In turn, the within-class scatter matrix will become singular. To overcome these limitations, this paper proposes a new kernel machine-based one-parameter regularized Fisher discriminant (K1PRFD) technique. K1PRFD is developed based on our previously developed one-parameter regularized discriminant analysis method and the well-known kernel approach. Therefore, K1PRFD consists of two parameters, namely the regularization parameter and kernel parameter. This paper further proposes a new method to determine the optimal kernel parameter in RBF kernel and regularized parameter in within-class scatter matrix simultaneously based on the conjugate gradient method. Three databases, namely FERET, Yale Group B, and CMU PIE, are selected for evaluation. The results are encouraging. Comparing with the existing LDA-based methods, the proposed method gives superior results.

Framelet Algorithms for De-Blurring Images Corrupted by Impulse Plus Gaussian Noise

This paper studies a problem of image restoration that observed images are contaminated by Gaussian and impulse noise. Existing methods for this problem in the literature are based on minimizing an objective functional having the l1 fidelity term and the Mumford-Shah regularizer. We present an algorithm on this problem by minimizing a new objective functional. The proposed functional has a content-dependent fidelity term which assimilates the strength of fidelity terms measured by the l1 and l2 norms. The regularizer in the functional is formed by the l1 norm of tight framelet coefficients of the underlying image. The selected tight framelet filters are able to extract geometric features of images. We then propose an iterative framelet-based approximation/sparsity deblurring algorithm (IFASDA) for the proposed functional. Parameters in IFASDA are adaptively varying at each iteration and are determined automatically. In this sense, IFASDA is a parameter-free algorithm. This advantage makes the algorithm more attractive and practical. The effectiveness of IFASDA is experimentally illustrated on problems of image deblurring with Gaussian and impulse noise. Improvements in both PSNR and visual quality of IFASDA over a typical existing method are demonstrated. In addition, Fast_IFASDA, an accelerated algorithm of IFASDA, is also developed.

Face Recognition by Regularized Discriminant Analysis

When the feature dimension is larger than the number of samples the small sample-size problem occurs. There is great concern about it within the face recognition community. We point out that optimizing the Fisher index in linear discriminant analysis does not necessarily give the best performance for a face recognition system. We propose a new regularization scheme. The proposed method is evaluated using the Olivetti research laboratory database, the Yale database, and the Feret database.

Structured Sparse Error Coding for Face Recognition With Occlusion

Face recognition with occlusion is common in the real world. Inspired by the works of structured sparse representation, we try to explore the structure of the error incurred by occlusion from two aspects: the error morphology and the error distribution. Since human beings recognize the occlusion mainly according to its region shape or profile without knowing accurately what the occlusion is, we argue that the shape of the occlusion is also an important feature. We propose a morphological graph model to describe the morphological structure of the error. Due to the uncertainty of the occlusion, the distribution of the error incurred by occlusion is also uncertain. However, we observe that the unoccluded part and the occluded part of the error measured by the correntropy induced metric follow the exponential distribution, respectively. Incorporating the two aspects of the error structure, we propose the structured sparse error coding for face recognition with occlusion. Our extensive experiments demonstrate that the proposed method is more stable and has higher breakdown point in dealing with the occlusion problems in face recognition as compared to the related state-of-the-art methods, especially for the extreme situation, such as the high level occlusion and the low feature dimension.

Face Recognition Using Dual-Tree Complex Wavelet Features

We propose a novel facial representation based on the dual-tree complex wavelet transform for face recognition. It is effective and efficient to represent the geometrical structures in facial image with low redundancy. Moreover, we experimentally verify that the proposed method is more powerful to extract facial features robust against the variations of shift and illumination than the discrete wavelet transform and Gabor wavelet transform.

Improved discriminate analysis for high-dimensional data and its application to face recognition

Many pattern recognition applications involve the treatment of high-dimensional data and the small sample size problem. Principal component analysis (PCA) is a common used dimension reduction technique. Linear discriminate analysis (LDA) is often employed for classification. PCA plus LDA is a famous framework for discriminant analysis in high-dimensional space and singular cases. In this paper, we examine the theory of this framework and find out that even if there is no small sample size problem the PCA dimension reduction cannot guarantee the subsequent successful application of LDA. We thus develop an improved discriminate analysis method by introducing an inverse Fisher criterion and adding a constrain in PCA procedure so that the singularity phenomenon will not occur. Experiment results on face recognition suggest that this new approach works well and can be applied even when the number of training samples is one per class.

Coupled Kernel Embedding for Low-Resolution Face Image Recognition

Practical video scene and face recognition systems are sometimes confronted with low-resolution (LR) images. The faces may be very small even if the video is clear, thus it is difficult to directly measure the similarity between the faces and the high-resolution (HR) training samples. Face recognition based on traditional super-resolution (SR) methods usually have limited performance because the target of SR may not be consistent with that of classification, and time-consuming SR algorithms are not suitable for real-time applications. In this paper, a new feature extraction method called coupled kernel embedding (CKE) is proposed for LR face recognition without any SR preprocessing. In this method, the final kernel matrix is constructed by concatenating two individual kernel matrices in the diagonal direction, and the (semi)positively definite properties are preserved for optimization. CKE addresses the problem of comparing multimodal data that are difficult for conventional methods in practice due to the lack of an efficient similarity measure. Particularly, different kernel types (e.g., linear, Gaussian, polynomial) can be integrated into a uniform optimization objective, which cannot be achieved by simple linear methods. CKE solves this problem by minimizing the dissimilarities captured by their kernel Gram matrices in the LR and HR spaces. In the implementation, the nonlinear objective function is minimized by a generalized eigenvalue decomposition. Experiments on benchmark and real databases show that our CKE method indeed improves the recognition performance.

Rapid and brief communication: Inverse Fisher discriminate criteria for small sample size problem and its application to face recognition

This paper addresses the small sample size problem in linear discriminant analysis, which occurs in face recognition applications. Belhumeur et al. [IEEE Trans. Pattern Anal. Mach. Intell. 19 (7) (1997) 711-720] proposed the FisherFace method. We find out that the FisherFace method might fail since after the PCA transform the corresponding within class covariance matrix can still be singular, this phenomenon is verified with the Yale face database. Hence we propose to use an inverse Fisher criteria. Our method works when the number of training images per class is one. Experiment results suggest that this new approach performs well.